Learn about the commutative property of addition by stacking and arranging ten blocks in different ways

Grades K-2

**Introduction**

Learning about the commutative properties of numbers is an elementary skill for later development of equations and problem solving. Students will learn how to express different combinations of numbers using a visual model and be able to write word sentences about the combinations.

**Preparation**

Manipulatives may be used in addition to the computer for reinforcement if desired.

**Procedure**

The teacher demonstrates the use of GollyGee Blocks to visually express number combinations. Students are instructed to load ten cubes into a scene. The students will count out loud the number of small cubes placed on the screen to verify there are ten.

The teacher demonstrates and discusses the different Color and Texture choices to encourage a wide variety of block arrangements. This step is lots of fun! Be sure students don't spend all their time on designing unique blocks. Instead keep them moving along to the next steps.

Using the Stacking tool, the children stack some blocks on top of one another, creating several stacks with the existing blocks.

Next, the students count the number of blocks in each stack and write down the number sentence (equation) showing the total sum of blocks (e.g., 4 blocks + 6 blocks is (equals) ten blocks).

Students use the Rotation arrows to move to the back of the scene. Students need to count out the number of blocks and write the new number equation (number sentence) for the sum. The total will be the same no matter where the stacks are located or what the viewing perspective is, an interesting method of teaching commutative properties.

Students print out different combinations of numbers to make the same total. Journal entries should be made if math journals are used by the class.

**Evaluation**

Teacher observation and student communication give the quickest and most natural feedback. This mode indicates the children's understanding level as they work through the activity.

After first teaching /introduction lesson, the teacher should be able to begin observing concept and math development levels. The teacher should have the students check out each other's work and share out ideas they compare as they show and discuss their representations.

Use this activity as remedial practice for second graders needing review and more concrete representation level math activities near the beginning of the year.

**Extensions**

The students may write and illustrate their number sentence for display using the overhead projector.

Students can share ideas for different representations for ways to make ten. Are there other possibilities for different ways to make ten? Discuss and list how many.

Students should try taking an equation with three or more addends and count the number of equivalent ways (possibilities) that number sentence can be written or depicted.

Use one number as a sample for the whole class to list possibilities of combinations for showing a number (e.g., the number 12 can be represented in how many different combinations of three addends 4+2+6). List the combinations with everyone's help!

A class book can be created of the Ways To Make Ten.

Extend these to other numbers through 20 for the second graders.

Students can discuss and match the turn around properties of equations with two addends for the class to see, record, and extend understanding.

**Tips**

Many math textbooks and programs teach the beginning idea of the commutative properties as turn-arounds. Naming the concept its mathematical name Commutative Property comes around mid third to mid fourth grader level. And, some first graders will be able to list all possibilities of addends to show ten if called ways to make ten. This would usually occur near the end of first or middle of second grade. It is suggested that the teacher not use this as an evaluation measure, only as enrichment.